SaddleSum
SaddleSum
Term enrichment analysis facilitates biological interpretation by assigning to experimentally/computationally obtained data annotation associated with terms from controlled vocabularies. This process usually involves obtaining statistical significance for each vocabulary term and using the most significant terms to describe a given set of biological entities, often associated with weights. Many existing enrichment methods require selections of (arbitrary number of) the most significant entities and/or do not account for weights of entities. Others either mandate extensive simulations to obtain statistics or make assumptions about data distribution that need not be justifiable. In addition, most methods have difficulty assigning correct statistical significance to terms with few entities.
Implementing the well-known Lugananni-Rice formula, we have developed a novel approach, called SaddleSum, that is free from all these undesirable constraints. It approximates the distribution of sum of weights asymptotically by saddlepoint method to arrive at analytically and computationally tractable form.
We evaluated SaddleSum against several existing methods and demonstrated its ability to adapt equally well to distributions with widely different properties. With entity weights properly taken into account, SaddleSum is internally consistent and stable with respect to the choice of number of most significant entities selected. Making few assumptions on the input data, the proposed method is universal and can thus be applied to areas beyond analysis of microarrays, such as deep sequencing, quantitative proteomics and in silico network simulations. SaddleSum also provides a term-size dependent score distribution function that gives rise to accurate statistical significance even for terms with few entities. As a consequence, SaddleSum enables researchers to place confidence in its significance assignments to small terms that are often biologically most specific.
Suppose that you have obtained some measurements for a number of genes or proteins in an organism. These can be gene expression log-ratios or values computed through some simulation. The problem now is to biologically interpret your experiment, that is, to link it to known terms and concepts.
One way to do so is to obtain a controlled vocabulary that covers the domain of your investigation and serves as basis for annotation of the genes from your organism. This means that every term in that vocabulary is associated with one or more genes; the term describes its associated genes. Your original problem is now transformed to the question of finding what terms best describe your overall measurements.
Let us further assume that gene measurements, which we will call weights, indicate relative importance of genes. If that is not so, for example if all highly expressed genes should be treated equally, you can transform your values so that this assumption holds and continue from there. A natural way to express the importance of each vocabulary term is to compute its score as the sum of weights of all genes mapping to that term.
Unfortunately, the score just calculated is not a good way to compare terms. Different terms may contain different numbers of genes and hence cover different parts of your measurement set. Thus, it may be possible that difference in scores of two terms is only due to their coverage. Normalizing by the number of genes may help but does not go far enough; there is still a question of the scale of the scores and their distribution.
The standard approach to this issue is statistical: we want to know the probability of a given score occurring by chance with respect to some null distribution. This probability is known as P-value and can be used as the statistical significance of the term. Note that there is a null distribution here associated with each term. In our case, it is reasonable to assume that the scores are built by summing m independently and identically distributed weights, where m is the number of genes mapping to the term. If the term P-value is sufficiently small, say 0.01, we can conclude that it is very unlikely that term score has arisen by chance. Therefore, we are able to interpret our dataset using that term.
SaddleSum is a tool that automates the above procedure. It requires a term database and a collection of gene labels associated with weights. It outputs the most statistically significant terms together with their estimated statistical significance. To compute P-values, SaddleSum first estimates the distribution of weights using all the supplied weights. Then using this estimated distribution, it approximates the P-value of a score using the asymptotic saddlepoint approach developed by Lugananni and Rice. This estimate is extremely accurate, even for terms with very small number of associated genes or for very small P-values.
To correct for the fact that a term database usually has many terms that enhance the chance of random matches, it is necessary to perform multiple hypothesis testing correction. SaddleSum uses Bonferroni correction for multiple hypothesis testing, where raw term P-values are multiplied with the effective database size to give E-values. We define the effective database size as the number of terms in the term database that map to at least k genes corresponding to selected nodes, where k is the minimum term size. This parameter is calculated at the time of the query. By default, the calculated value is used to compute E-values but you can can override it by changing the corresponding form entry. For example, raw P-values can be displayed by setting the effective database size to 1.
SaddleSum can be used through three interfaces: command line (standalone version), web and as a Cytoscape plugin.
The standalone version is written completely in the C programming language and has no dependencies beyond the gcc compiler and GNU make (although it is likely that it can be adapted to compile using other development tools). It provides a command line interface and uses term databases in a simple tab-delimited format (GMT) as well as in SaddleSum’s own ETD (Extended Term Database) format.
The web version provides a wrapper for the standalone version via a web form. The server script that interacts with the standalone version is written in Python programming language and is a part of qmbpmn-tools package, which also includes ITM Probe, a framework for analysis of information flow in interaction networks based on random walks. The qmbpmn-tools package depends on a number of external Python libraries and on the Graphviz suite for visualizing graphs.
Cytoscape is an open source platform for complex network analysis and visualization written in Java programming language. Apart for a rich set of graph visualization tools, it provides an interface for externally written plugins that provide additional functionality such as network analysis algorithms, database import and functional enrichment analysis. Cytoscape users are therefore able to combine algorithms and data from different sources to perform complex network-based analyses.
CytoSaddleSum is a Cytoscape plugin that enables SaddleSum queries from Cytoscape platforms. It can interact either with a locally installed command-line program directly, or through our web server. The results are presented as a Cytoscape network view showing term relationships. Term statistics, written to node attributes in the relationship network, can be manipulated by the user.